You need to have an idea of what fits first. That way you don't have to waste your time on tiny bikes for short people, or huge bikes for tall people, unless you are very short or very tall.

After that, it is all about knowing what was good when new, and looking for a well maintained fairly clean bike. The bike could be 3 or 4 years old or 15 or 20 years old. It isn't so much the model year, but the condition. Stay away from anything rusty, dented, or beat up. Wheels should spin true. Chain won't be squeaky clean, but it shouldn't be filthy or rusty either. Cranksets should turn smoothly. Headsets should move smoothly. Tires should have some tread, and not be cracked at the sidewallsYou know the well regarded brands, right? Cannondale, Giant, Trek, Specialized, Bianchi, Raleigh, Jamis, Surly. Diamondback, GT and Schwinn might be good, but you need to know what year and what model, as some models were crappy department store models and some were quality bike shop models. This is not a comprehensive list. There are other smaller brands that are good but it is a start.